Answer: d = -16 . _______________________________________________________ Explanation: ____________________________________________________
Given: 0.2 (d − 6) = 0.3d + 5 − 3 + 0.1 d ; Solve for "d" ; _________________________________________ → Note the distributive property of multiplication: ____________________________________________ a (b + c) = ab + ac ; a (b − c) = ab − ac ; ________________________________________ As such, we can expand the left-hand side of the question: ______________________________________________ → 0.2 (d − 6) = (0.2 *d) − (0.2 *6) = 0.2 d − 1.2; ________________________________________ And rewrite the entire equation: ________________________________________ → 0.2 d − 1.2 = 0.3d + 5 − 3 + 0.1 d ; __________________________________________ → Let us multiply the ENTIRE equation (both sides) by "10"; to get rid of the decimals: _________________________________________ → 10 * {0.2 d − 1.2 = 0.3d + 5 − 3 + 0.1 d} ; ___________________________________________ → 2d − 12 = 3d + 50 − 30 + 1d ;
→ Combine the "like terms", +3d , +1d ; to get 4d; on the 'right-hand side' of the equation ; and rewrite:
→ 2d − 12 = 4d + 50 − 30 ;
→ Now add "12"; and subtract "2d" from EACH SIDE of the equation;
→ 2d − 12 + 12 − 2d= 4d + 50 − 30 + 12 − 2d ;
→ 0 = 2d + 32 ; ↔ 2d + 32 = 0 ;
→ Subtract "32" from each side of the equation: _________________________________________________________ → 2d + 32 − 32 = 0 − 32 ;
→ 2d = - 32 __________________________________ → Now, divide EACH side of the equation by "2" ; to isolate "d" on ONE side of the equation; and to solve for "d" ; ____________________________________________________ → 2d / 2 = - 32 / 2 ; _________________________________________ → d = - 16 ; which is our answer. _______________________________________________________ Let us check our answer by plugging this value for "d" in the original equation to see if the equation holds true when "d = -16" ; ___________________________________________________ → 0.2 (d − 6) = 0.3d + 5 − 3 + 0.1 d ; _______________________________________________ → Let us start with the "left-hand side". _______________________________________ → 0.2 (d − 6) ; ↔ 0.2*(-16 − 6) ; ↔ 0.2*(-22) = -4.4. _____________________________________________ When "d" = -16 in the right-hand side of the equation, is the result, "-4.4" ??? _______________________________________________ → 0.3d + 5 − 3 + 0.1 d = ? -4.4 ??? ________________________________________ → (0.3 * -16) + 5 − 3 + (0.1 * -16) =? -4.4??? _____________________________________________ → (-4.8) + 5 − 3 + (-1.6) = ? -4.4???? ___________________________________________ → (-4.8) + 5 − 3 − (1.6) = ? -4.4????
